context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 510 | task_name stringclasses 6
values | metadata dict | model_outputs stringlengths 563 148k |
|---|---|---|---|---|---|---|
[
{
"content": "Problem: Among the 900 residents of Aimeville, there are 195 who own a diamond ring, 367 who own a set of golf clubs, and 562 who own a garden spade. In addition, each of the 900 residents owns a bag of candy hearts. There are 437 residents who own exactly two of these things, and 234 residents wh... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | AIME24 | {
"expected_answer": "73",
"problem_id": "aime24-0",
"reference_solution": "Let $w,x,y,z$ denote the number of residents who own 1,2,3 and 4 of these items, respectively. We know $w+x+y+z=900$ , since there are 900 residents in total. This simplifies to $w+z=229$ , since we know $x=437$ and $y=234$ . Now, w... | Alright, let's tackle this problem step by step. It's about figuring out how many people in Aimeville own all four items: a diamond ring, a set of golf clubs, a garden spade, and a bag of candy hearts. We know the total number of residents is 900, and we have some specific numbers about how many own certain combination... |
[
{
"content": "Problem: A list of positive integers has the following properties: $\\bullet$ The sum of the items in the list is $30$ . $\\bullet$ The unique mode of the list is $9$ . $\\bullet$ The median of the list is a positive integer that does not appear in the list itself. Find the sum of the squares... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 1 | AIME24 | {
"expected_answer": "236",
"problem_id": "aime24-1",
"reference_solution": "The third condition implies that the list's size must be an even number, as if it were an odd number, the median of the list would surely appear in the list itself. Therefore, we can casework on what even numbers work. Say the size is 2.... | Alright, let's tackle this problem step by step. It's a bit tricky, but I'll try to break it down. So, we have a list of positive integers with three properties:
1. The sum of the items is 30.
2. The unique mode is 9.
3. The median is a positive integer that doesn't appear in the list itself.
We need to find the sum ... |
[
{
"content": "Problem: Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is $999$ , and the sum of the three numbers formed by reading top to bottom is $99$ . The grid below is an example of such an arrangement because $8+99... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 2 | AIME24 | {
"expected_answer": "45",
"problem_id": "aime24-2",
"reference_solution": "Consider this table: $\\begin{array}{|c|c|c|} \\hline a & b & c \\\\ \\hline d & e & f\\\\ \\hline \\end{array}$ We note that $c+f = 9$ , because $c+f \\leq 18$ , meaning it never achieves a unit's digit sum of $9$ otherwise. Since no... | Alright, so I have this problem where I need to figure out how many ways to place digits in a 2x3 grid. The conditions are that when you read the numbers left to right, their sum should be 999, and when you read them top to bottom, their sum should be 99. Hmm, okay. Let me try to break this down.
First, let me visuali... |
[
{
"content": "Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n \\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\] \\[\\log_2\\left({y \\over xz}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | Alright, so I have this problem where I need to find the value of |log₂(x⁴y³z²)| given a system of logarithmic equations. The equations are:
1. log₂(x / (yz)) = 1/2
2. log₂(y / (xz)) = 1/3
3. log₂(z / (xy)) = 1/4
And then express this value as m/n where m and n are coprime, and find m + n.
Okay, let me start by reca... |
[
{
"content": "Problem: Let ABCDEF be a convex equilateral hexagon in which all pairs of opposite sides are parallel. The triangle whose sides are extensions of segments AB, CD, and EF has side lengths 200, 240, and 300. Find the side length of the hexagon.\nMark your solution with \\boxed\nAnswer:",
"role":... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 4 | AIME24 | {
"expected_answer": "80",
"problem_id": "aime24-4",
"reference_solution": "Draw a good diagram!\nLet $AF \\cap BC$ , $BC \\cap DE$ , and $AF \\cap DE$ be K, L, and M, respectively. Let $KL=200, KM=300, ML=240$ . Notice that all smaller triangles formed are all similar to the larger $(200,240,300)$ triangl... | Alright, so I have this problem about a convex equilateral hexagon where all pairs of opposite sides are parallel. The triangle formed by extending the sides AB, CD, and EF has side lengths 200, 240, and 300. I need to find the side length of the hexagon.
Hmm, okay. Let me start by understanding the problem better. Fi... |
[
{
"content": "Problem: Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$ . Bob's list has 2024 sets. Find the sum of the elements of A.\nMark your solution with \\boxed\nAnswer:",... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | AIME24 | {
"expected_answer": "55",
"problem_id": "aime24-5",
"reference_solution": "Let $k$ be one of the elements in Alices set $A$ of positive integers. The number of sets that Bob lists with the property that their maximum element is k is $2^{k-1}$ , since every positive integer less than k can be in the set or o... | Alright, let's tackle this problem step by step. So, Alice chooses a set \( A \) of positive integers. Then Bob lists all finite nonempty sets \( B \) of positive integers where the maximum element of \( B \) is in \( A \). Bob ends up with 2024 sets. We need to find the sum of the elements of \( A \).
Hmm, okay. Let ... |
[
{
"content": "Problem: Let $N$ be the greatest four-digit positive integer with the property that whenever one of its digits is changed to $1$ , the resulting number is divisible by $7$ . Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$ . Find $Q+R$ .\nMark ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | AIME24 | {
"expected_answer": "699",
"problem_id": "aime24-6",
"reference_solution": "We note that by changing a digit to $1$ for the number $\\overline{abcd}$ , we are subtracting the number by either $1000(a-1)$ , $100(b-1)$ , $10(c-1)$ , or $d-1$ . Thus, $1000a + 100b + 10c + d \\equiv 1000(a-1) \\equiv 100(b-1... | Alright, so I have this problem where I need to find the greatest four-digit positive integer, N, with a specific property. The property is that whenever one of its digits is changed to 1, the resulting number is divisible by 7. Then, I have to find Q and R, where Q is the quotient and R is the remainder when N is divi... |
[{"content":"Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ ar(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 7 | AIME24 | {"expected_answer":"127","problem_id":"aime24-7","reference_solution":"First, let's consider a secti(...TRUNCATED) | "Alright, so I have this problem about a torus and a sphere. Let me try to visualize it first. The t(...TRUNCATED) |
[{"content":"Problem: There is a collection of $25$ indistinguishable white chips and $25$ indis(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 8 | AIME24 | {"expected_answer":"902","problem_id":"aime24-8","reference_solution":"The problem says \"some\", so(...TRUNCATED) | "Alright, so I have this problem where I need to figure out the number of ways to place some white a(...TRUNCATED) |
[{"content":"Problem: Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\ove(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 9 | AIME24 | {"expected_answer":"468","problem_id":"aime24-9","reference_solution":"By Euler's formula $OI^{2}=R(...TRUNCATED) | "Alright, so I have this problem about triangle ABC with circumcenter O and incenter I. The problem (...TRUNCATED) |
End of preview. Expand in Data Studio
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Check out the documentation for more information.
mlfoundations-dev/DeepSeek-R1-Distill-Qwen-32B_1743609165_eval_0981
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME24 | AIME25 | AMC23 | MATH500 | GPQADiamond | LiveCodeBench |
|---|---|---|---|---|---|---|
| Accuracy | 74.7 | 50.0 | 96.5 | 90.0 | 65.8 | 72.3 |
AIME24
- Average Accuracy: 74.67% ± 2.42%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 73.33% | 22 | 30 |
| 2 | 76.67% | 23 | 30 |
| 3 | 83.33% | 25 | 30 |
| 4 | 73.33% | 22 | 30 |
| 5 | 66.67% | 20 | 30 |
AIME25
- Average Accuracy: 50.00% ± 1.33%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 53.33% | 16 | 30 |
| 2 | 46.67% | 14 | 30 |
| 3 | 53.33% | 16 | 30 |
| 4 | 50.00% | 15 | 30 |
| 5 | 46.67% | 14 | 30 |
AMC23
- Average Accuracy: 96.50% ± 0.55%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 95.00% | 38 | 40 |
| 2 | 97.50% | 39 | 40 |
| 3 | 97.50% | 39 | 40 |
| 4 | 97.50% | 39 | 40 |
| 5 | 95.00% | 38 | 40 |
MATH500
- Accuracy: 90.00%
Accuracy Questions Solved Total Questions 90.00% 450 500
GPQADiamond
- Average Accuracy: 65.82% ± 1.13%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 63.13% | 125 | 198 |
| 2 | 66.67% | 132 | 198 |
| 3 | 67.68% | 134 | 198 |
LiveCodeBench
- Average Accuracy: 72.28% ± 0.75%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 72.60% | 371 | 511 |
| 2 | 73.39% | 375 | 511 |
| 3 | 70.84% | 362 | 511 |
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